Two parallel slits are illuminated by light composed of two wavelengths. One wav
ID: 1380922 • Letter: T
Question
Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is ?A = 630 nm. The other wavelength is ?B and is unknown. On a viewing screen, the light with wavelength ?A = 630 nm produces its fifth-order bright fringe at the same place where the light with wavelength ?Bproduces its fifth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength? Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is ?A = 630 nm. The other wavelength is ?B and is unknown. On a viewing screen, the light with wavelength ?A = 630 nm produces its fifth-order bright fringe at the same place where the light with wavelength ?Bproduces its fifth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?Explanation / Answer
when you have a bright fringe, the optical path difference that we will call delta equals the order * lambda
when you have dark fringe, the optical path difference equals (the order +1/2) * lambda
if you consider the same place on the screen, delta doesn't change
which means deltaA = 5 * lambdaA = lambdaB = (5+1/2)* lambdaB
so lambdaB = 10/11* lambdaA = 10*630/11 =572.72nm
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